# Determining the Specific Heat Capacity of Air by yurtgc548

VIEWS: 0 PAGES: 22

• pg 1
```									Determining the Specific Heat
Capacity of Air
Contents
Ⅰ： Aim
Ⅱ： Introduction
Ⅲ： Theory
Ⅳ： Experimental Process
Ⅴ： Instruments and Data Table
Ⅰ： Aim

• To measure the specific heat ratio of
air by the method of adiabatic
expansion.
• To learn how to use the temperature
sensor and the pressure sensor.
Ⅱ：Introduction
• The heat capacity ratio or adiabatic index or ratio of
specific heats, is the ratio of the heat capacity at
constant pressure (CP) to heat capacity at constant
volume (CV). It is sometimes also known as the
isentropic expansion factor and is denoted by γ
(gamma).

where, C is the heat capacity or the specific heat
capacity of a gas, suffix P and V refer to constant
pressure and constant volume conditions respectively.
Ideal gas relations
• For an ideal gas, the heat capacity is constant
with temperature. Accordingly we can express
the enthalpy as H = CPT and the internal
energy as U = CVT. Thus, it can also be said
that the heat capacity ratio is the ratio between
the enthalpy to the internal energy:
Ideal gas relations
• Furthermore, the heat capacities can be
expressed in terms of heat capacity ratio ( γ )
and the gas constant ( R ):

and

So：
Relation with degrees of freedom
• The heat capacity ratio ( γ ) for an ideal gas can be
related to the degrees of freedom ( f ) of a molecule by:

• Thus we observe that for a monatomic gas, with three
degrees of freedom:

• while for a diatomic gas, with five degrees of freedom
(at room temperature):
E.g.
• The terrestrial air is primarily made up of diatomic
gasses (~78% nitrogen (N2) and ~21% oxygen
(O2)) and, at standard conditions it can be
considered to be an ideal gas. A diatomic
molecule has five degrees of freedom (three
translational and two rotational degrees of
freedom). This results in a value of
Ratio of Specific Heats for
some common gases
Gas             Ratio of Specific Heats
Carbon Dioxide                 1.3
Helium                     1.66
Hydrogen                    1.41
Methane or Natural Gas            1.31
Nitrogen                   1.4
Oxygen                     1.4
Standard Air                 1.4
One Standard Atmosphere
Common Pressure Units frequently used as
alternative to "one Atmosphere"
• 76 Centimeters (760 mm) of Mercury
• 10.332 Meters of Water
• 101.33 Kilopascal
Note: Standard atmosphere is a pressure defined as
101'325 Pa and used as unit of pressure (symbol:
atm).
The original definition of “Standard Temperature
and Pressure” (STP) was a reference temperature
of 0 °C (273.15 K) and pressure of 101.325 kPa (1
atm).
Ⅲ：Theory
•   Ideal gas law
– The state of an amount of gas is determined by its
pressure, volume, and temperature according to the
equation:

where
P  is the absolute pressure of the gas,
V  is the volume of the gas,
n is the number of moles of gas,
R  is the universal gas constant,
T   is the absolute temperature.
The value of the ideal gas constant, R, is found to be as
follows.
R = 8.314472J·mol−1·K−1
Calculations
Process           Constant       Equation
Isobaric process     Pressure      V/T=constant

Isochoric process     Volume       P/T=constant

Isothermal
Temperature    PV=constant
process
Isentropic
process                        PVγ=constant
(Reversible         Entropy     Pγ-1/Tγ=constant
process)
Isotherms of an ideal gas

T: high

T: low
Ⅳ: Experimental process

expansion           (pressure
increase)

Ⅰ(P1,T0)        Ⅱ(P0,T1)        Ⅲ(P2,T0)
Calculations

Equation 1
Calculations
Isochoric process (pressure increase).
Ⅱ(P0,T1)------Ⅲ(P2,T0)

Equation 2
Calculations
Through equation 1 and 2

Equation 3
Ⅴ:Instruments and data table
Testing Instrument
Sensitivity
• The Pressure Sensor:20mV/kPa

• The Temperature Sensor:5mV/K
Data table
P0（kPa         ΔP1      P1     ΔP1   P2 （kPa
T0                                    γ
）          (mV )   (kPa)   (mV)      ）

1

2

3
101.30
4

5

6
Result

```
To top